Both are correct. I would say the first, "I got two questions for you," is actually more common in modern spoken American English. Lorenzo is correct, if you are writing it, or speaking formally, use "I've got.." or more simply, "I have two questions for you."

You´re right, but native speakers are lazy and sloppy. They often use the first variant. I always use the second. It´s a question of personal style, how correctly you want to speak, and your audience.

Technically "got" and "gotten" by themselves are not verbs. They need "has, have, had" etc. However, many native speakers use "got" incorrectly. I suggest using "have" instead. edited typo (speaker to speakers).

I would structure that sentence like , I have two questions for you. This way it is more formal and fluent.